Is there a modifier to transform proportionally along a circle? (for tri-lateral symmetry)
Thanks to @Jerryno, I have an even more general solution than I was hoping for.  In fact, it addresses any degree of symmetry that I need.  Here are the details.

Here is my base geometry with only a subsurf modifier:



Notice it also shows a Bezier circle that I will be using.

1 - Add an Array modifier with a fixed count of 3.  Notice that Merge is checked.



This gives a result like:



2 - Next we want to use a Curve modifier to bend things around the circle.



This gives something like:



3 - Don't fret about the gap.  In order to close the gap, select the Bezier Circle and type "3/pi" in the X Scale and Y Scale.  Since Blender interprets the Python expression it will show .955 in the cells as in:



Which gives the very satisfying result of:



Interestingly, if you change the Array modifier fixed count to anything, N, and change the scale on the circle to N/pi, you can get higher degrees of symmetry (e.g. w/ N = 5):



How cool is that?!  (Man, I love Blender!)

One more thing might make this even more convenient.  Since we have an odd number (3 in my case) of repeats, it isn't truly symmetrical.  When I edit, it looks like...



If you want this edit to be truly symmetrical (i.e. each edit affects 6 analogous areas in the final geometry), then put a Mirror modifier for the X axis first in the modifier stack and only start with half of the original geometry.  And we get...



So to summarize, the full recipe of modifiers for this N-lateral symmetry is:

1 - Mirror Modifier in X

2 - Array Modifier w/ a fixed count of N

3 - Curve modifier with a Bezier Circle

4 - Make sure the Bezier circle has a radius of N/pi